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Research Centre for International Economics
Working Paper: 2014008
Title of Paper The Penn Effect within a Country – Evidence from
Japan
Authors’ List
Yin-Wong Cheung, City University of Hong Kong, and Eiji Fujii,
Kwansei Gakuin University
Abstract
To control for product quality and exchange rate effects, we use
the Japanese regional data to study the Penn effect – the positive
relationship between price and income levels. Comparable with the
evidence from international data, the Penn effect is significant in
the Japanese prefectural data and driven mainly by the prices of
nontradables. We draw upon studies of productivity and economic
density to explain the positive price-income relationship, and find
that the empirical economic density variables explain the
variability of the Japanese prefectural (relative) prices quite
well. © 2014 by Yin-Wong Cheung. All rights reserved. Short
sections of text, not to exceed two paragraphs, may be quoted
without explicit permission provided that full credit, including ©
notice, is given to the source.
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The Penn Effect within a Country –
Evidence from Japan
Yin-Wong Cheung
Eiji Fujii
Abstract
To control for product quality and exchange rate effects, we use
the Japanese regional data to study the Penn effect – the positive
relationship between price and income levels. Comparable with the
evidence from international data, the Penn effect is significant in
the Japanese prefectural data and driven mainly by the prices of
nontradables. We draw upon studies of productivity and economic
density to explain the positive price-income relationship, and find
that the empirical economic density variables explain the
variability of the Japanese prefectural (relative) prices quite
well.
JEL Classifications: F31, F34, F36
Keywords: Agglomeration, Economic Density, Price and Income
Relationship, Productivity
Differential, Tradables and Non-Tradables.
Acknowledgments: We are grateful to Francis Teal, the managing
editor, and two anonymous referees. Their comments and suggestions
greatly improved the manuscript. We also thank Michael Funke, Jan
Fidrmuc, Stephan Hansen, and participants of the CESifo Macro,
Money and International Finance Conference for their comments and
suggestions on earlier drafts of the paper. Fujii gratefully
acknowledges the financial support of the Japan Society for the
Promotion of Sciences (Grant-in-Aid for Scientific Research
20530263, 25285087). Corresponding addresses: Yin-Wong Cheung:
Department of Economics & Finance, City University of Hong
Kong,
Hong Kong. E-mail: [email protected] Eiji Fujii: School of
Economics, Kwansei Gakuin University, Hyogo, Japan. E-mail:
[email protected].
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1. Introduction
The Penn effect refers to the robust empirical positive
association between national
price levels and real per capita incomes that is documented by a
series of Penn studies
including Kravis et al. (1978), Kravis and Lipsey (1983, 1987),
and Summers and Heston
(1991). The accumulated evidence attests that compared with poor
countries, rich countries
tend to have higher price levels. The positive association
between income and price levels is
considered a fundamental fact of economics (Samuelson, 1994) and
conventional wisdom in
international economics (Bergin, 2009).
Most studies analyzing the price-income relationship have relied
on data derived from
the surveys conducted by the International Comparison Program
(ICP). Since its
establishment in 1968, the ICP has conducted periodic surveys on
national prices. The survey
results are used to construct internationally comparable price
indices and national output data.
The ICP has expanded the country sample and product coverage,
and improved the survey
methodology and data processing procedure over the last few
decades to enhance the
reliability of the survey.1 Despite the ICP’s continuing
efforts, it remains a daunting task to
aggregate and compare prices of vastly dissimilar products from
countries of different
economic characteristics, and over time (Deaton and Heston,
2010).
Several factors contribute to the difficulty of constructing
internationally comparable
data. For instance, national price level comparison becomes
quite tricky, if not infeasible,
when countries differ substantially in their output structures
and consumption patterns. These
differences are not uncommon between countries at different
stages of development and with
different cultural backgrounds. For a given product, a
meaningful comparison of its prices in
different countries has to control for its quality attributes;
actual or perceived. It is quite
difficult to quantify quality differentials for nontradables
such as locally provided services.
To alleviate the concerns regarding data incompatibility, the
current study investigates
the price and income relationship using Japanese regional data.
The Japanese data offer a few
desirable features. For instance, the price data are collected
from national surveys that are
designed to cover products of the same quality and quantity
attributes across locations.
Further, availability of disaggregated price series enables us
to examine behavior of sectoral
1 The changes in the survey setup led to considerable data
revisions that have profound implications for estimates of growth
rates, growth determinants, poverty measures, and inequality
indicators; see, for example, Johnson et al. (2009), Milanovic
(2009), Chen and Ravallion (2010a, 2010b), Ciccone and Jarocinski
(2010), and Ponomareva and Katayama (2010). On the Penn effect,
Cheung et al. (2009) and Fujii (2013a) illustrate that, although
the positive price-income relation survives data revisions, the
magnitude of the estimated income effect has been noticeably
changed.
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prices. The income data are compiled under identical accounting
and tax systems. While
consumption bundles may still differ by regions, the degree of
consumption homogeneity
within Japan is arguably higher than that across countries. In
addition, the intra-Japanese
comparison is free from the exchange rate volatility effect that
sometimes inflicts
cross-country comparison.
There are no legal restrictions on either goods or factor flows
between regions within
Japan. The condition has two implications. First, unlike the
international cases, the
intra-national price-income relationship is not affected by
differences in policies on trade and
factor flows. Thus, it is relatively easy to interpret results
based on intra-national data.
Second, while free trade enhances goods price convergence, free
factor movement can
generate equalizing pressure on prices and qualities of local
services across regions.2 Of
course, the net effect of goods and factor flows depends on the
de facto mobility rather than
de jure restrictions because implicit barriers and frictions
exist even within a country.3 Given
these differences, it is of interest to compare intra-national
estimates to international ones.
In addition to data features, the current study takes an
alternative approach and draws
upon theories on productivity and economic density (Ciccone and
Hall, 1996) to explain the
intra-Japan Penn effect. Specifically, the economic density that
significantly affects labor
productivity is used to explain the price-income relationship
observed in the Japanese data.
Because good quality regional productivity data in Japan are
scarce, the empirical economic
density measure offers a good alternative to assess the
relevance of the well-known
productivity differential effect à la Balassa (1964) and
Samuelson (1964).
To anticipate the results, we find that, across the Japanese
regions, the price and
income levels are significantly positively associated with each
other. That is, the Penn effect,
commonly documented with international data, is also a staple
feature of the intra-Japanese
data. Our attempts to account for the intra-Japan price-income
relationship offer some
evidence that the Balassa-Samuelson (B-S) effect retains its
relevance in the intra-national
context. First, as implied by the usual B-S argument, the
positive price-income association is
driven essentially by prices of nontradables rather than those
of tradables. Further, we find
that price differentials across regions are significantly
determined and explained by
2 In principle, households can migrate to areas where quality
services are cheaper ceteris paribus. Private service-providers can
also choose their locations. The adjustment across regions may take
place in terms of either price, quality or both. 3 For instance,
factors such as uneven distribution of industrial locations,
climatic differences, and family ties within a region may work as
implicit barriers for labor flow. Also, non-negligible transport
cost generates market friction for flow of products.
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differences in regional economic density characteristics. Under
the assumption that economic
density is a proxy of productivity, our finding is consistent
with the presence of the B-S effect
in the Japanese data. Nonetheless, the effect of economic
density could have a broader
interpretation than the B-S effect because, in addition to the
supply-side effect, economic
density can affect relative prices of nontradables via the
demand-side channel.
The remainder of this paper is organized as follows. Section 2
provides a brief
background discussion, describes the data, and defines the
empirical variables. Section 3
presents the empirical price-income relationship between the
Japanese prefectures. The
results are then compared to those obtained from international
data. Section 4 investigates the
implications of tradability and productivity differentials using
data on different product
categories. In section 5, we evaluate the role of economic
density in explaining the
price-income relationship within Japan. Some concluding remarks
are offered in Section 6.
2. Preliminaries
2.1 Aggregate Price Level
At the risk of over-simplification, suppose region j ’s
aggregate price level in period t,
in logarithm, is given by
, , , , , (1 )j t N j t T j tp p p , (1)
where , ,N j tp is the price of nontradables, , ,T j tp is the
price of tradables, and defines the
weights of the price components. Similarly, the logged aggregate
price level of region j* is
*, , *, , *, * (1 *)j t N j t T j tp p p . (2)
To facilitate comparison, the exchange rate of the two regions’
currencies is used to convert
the two prices ,j tp and *,j tp into the same unit. For our
data, the regions are within Japan.
Thus, the exchange rate is fixed at unity, and ,j tp and *,j tp
can be directly compared.
Two additional assumptions commonly imposed are a) the two
prices use the same
weight; that is, = * , and b) the prices of tradables are the
same across different regions
so that , ,T j tp = , *,T j tp . Under these assumptions, the
conventional sectoral productivity
differential argument suggests that a less productive and,
hence, lower income region will
have a lower price of nontradables and a lower aggregate price
level.
The simple setting outlined above highlights a few controversial
issues that inflict
cross-country price comparison. In addition to exchange rate
volatility, the ability to compare
prices is impeded by the fact that aggregate price levels are
not necessarily compiled using an
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identical methodology. Further, prices of tradables are not
necessarily the same across
countries (Engel and Rogers, 1996). To further complicate the
situation, national aggregate
price levels comprise prices of individual products that have
heterogeneous, rather than
homogeneous, qualities across countries. The quality difference
does not only create a wedge
between prices of nontradables but also between prices of
tradables (Imbs et al., 2010).
2.2 Price Data
We use data from forty-seven prefectures in Japan. The Japanese
prefectures are
geographically defined administrative units largely
corresponding to, say, the States in the US.
Specifically, we use the Regional Difference Index of Consumer
Prices (RDICP) provided by
the Statistical Bureau of the Ministry of Internal Affairs and
Communications. The sources of
the price and other variables used in the following empirical
exercise are listed in the
Appendix. Instead of absolute price levels, these RDICP series
report prefectural consumer
price levels relative to the price level of the Tokyo central
area, which comprises twenty-three
districts of Tokyo prefecture. With central Tokyo as the common
reference, the RDICP data
allow us to gauge the price differentials of these forty-seven
Japanese prefectures.
The RDICP series are derived from the price information
collected by the Statistical
Bureau’s retail price survey. The survey records retail prices
of products and services that are
quite precisely defined. Examples of product and service
descriptions include “hen eggs
(color: white, size L, sold in pack of 10),” “men’s undershirt
(short sleeves, knitted, white,
100% cotton, [size] around the chest 88-96cm/MA (M), white,
ordinary quality, excluding
specially processed goods),” and “permanent wave charges
(including shampoo, cut, blow or
set) for short hair.” In many categories, product brands are
specified to ensure that prices are
recorded for identical products. For instance, ice cream prices
collected by the survey are
prices of “Häagen-Dazs vanilla (by Häagen-Dazs Japan), 120ml”.
The specificity of product
definition enhances price comparability and minimizes the role
of product heterogeneity in
explaining price differentials across prefectures.4
It is noted that the consumption tax is completely harmonized
across all regions in
Japan. In addition, the consumption patterns across these
Japanese prefectures are arguably
more homogeneous than those across countries. Thus, the
prefectural price differentials are
less subject to the effects of differential taxes and dissimilar
consumption patterns. In sum,
4 However, the perception of heterogeneity may be induced by
factors not controlled for in the survey, including the
characteristics of the store in which the products are sold.
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the use of these Japanese price data alleviates some of the
measurement and data
incompatibility issues raised in the previous subsection.
2.3 Basic Empirical Variables
The price variable used in this study is the deviation from the
prefectural average.
Specifically, a prefecture’s aggregate price level relative to
the average of prefecture price
levels, in logs, is measured by
47/lnln 471 ,,, j tjtjtj RPRPq , (3)
where tjRP , is prefecture j’s RDICP in period t. A similar
normalization procedure is also
applied to the per capita income data derived from information
on real gross prefectural
income and prefectural population provided by the Statistical
Bureau. The prefectural real per
capita income relative to the average of prefecture data, in
logs, is thus given by 47
, , , , ,1ln( / ) ln( / ) / 47j t j t j t j t j tjy Y H Y H ,
(4)
where ,j tY and ,j tH denote prefecture j’s real gross
prefecture income that includes net
factor payments from other prefectures, and population in period
t, respectively.5
Due to data availability, annual data from 1996 to 2008 are
considered. The time
averages of tjq , and ,j ty are listed in Table A-1 of the
Appendix. The relative aggregate
price level ranges from about five percentage points below
(-0.049, Okinawa) to more than
eight percent above (0.085, Tokyo) the average.
Inter-prefectural per capita income
differentials are far more substantial. As shown in the far
right column of Table A-1, the
time-average of per capita income relative to the average ranges
from -0.29 (Okinawa) to
0.50 (Tokyo). The income variation helps identify the income
effect on prices.
3. The Penn Effect within Japan
For each year, we estimate the Penn effect within Japan using
the canonical
cross-sectional bivariate specification
, , ,j t j t j tq y . (5)
5 The income and population data are available for Tokyo
prefecture but not for Tokyo central area. In addition to the
twenty-three districts in the center, Tokyo prefecture includes
twenty-six cities, five towns, and eight villages. The RDICP uses
Tokyo central area as the benchmark. The normalization procedure
adopted by (3) and (4) ensures the price and income data are
comparable.
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The time profile of the slope coefficient estimate ̂ and its
p-value obtained from
year-by-year cross-sectional regression are depicted in Figure
1.6 The estimated effect of
income on price is significantly positive throughout the sample
period. Even though the
year-by-year estimates display some variation, the parameter
stability tests indicate that these
estimates are not statistically different from each other. The
Penn effect is a robust empirical
feature of the Japanese data.
How does the Penn effect within Japan compare to the one
documented using
international data? Figure 2 plots the year-by-year income
effect estimates, ̂ s, obtained
from the corresponding data downloaded from the Penn World Table
(version 7.0) and the
World Development Indicator (January 2012), together with those
from the Japanese data.
The regressions based on international data use the US as the
reference country, and include
all countries with available observations. Although both PWT and
WDI are derived from the
same ICP 2005 survey information, they adopt different
approaches in their data compilation
methods. Thus, the estimates, ̂ s, from these international data
are not the same. Further,
while the Japanese regional data are CPI-based price data, the
PWT and WDI data are
GDP-based data. These differences should be considered in
comparing these ̂ -estimates.
In line with the extant literature, the Penn effect is
identified in the two international
datasets. As the plots indicate, the income effects exhibited by
these international data are
more substantial than the one by the Japanese data; that is,
compared with cross-country
behavior, the change in the income within Japan tends to induce
a smaller change in the price
level. Further, the evolution of the Japanese ̂ estimates is
discernibly different from those
of the other two ̂ -estimate series. Aside from these
differences, however, the three datasets
unanimously exhibit significant positive income effects on price
levels, which is a defining
signature of the empirical Penn effect. In sum, despite the
differences in data compilation and
construction methods, the Penn effect appears a prevalent
phenomenon in both the
cross-country and intra-Japan data.
The results thus far indicate that price and income levels of
Japanese prefectures are
positively related to each other – a relationship that is also
revealed by cross-country data.
The Penn effect in Japan is qualitatively similar though not
quantitatively identical to the
cross-country Penn effect.
6 Since both the dependent and independent variables are
deviations from the respective sample averages, the intercept is
zero by construction. Thus, the constant estimates are
insignificantly different from zero and not reported for
brevity.
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4. Prices of Nontradables and Tradables
A common explanation of the positive income effect on prices
draws on the different
price behaviors of nontradables and tradables and the difference
in sectoral productivities
(Balassa, 1964; Samuelson, 1964). In this section, we examine
the implications of the
tradable-nontrable dichotomy for the intra-Japan positive
price-income association.
Following (1) and (2) in Section 2.1, the relative price level
of two regions, in the
presence of a perfectly fixed exchange rate and under the
assumption of = * , is given by
*,j tp – ,j tp = ))(1()( ,,*,,,,*,, tjTtjTtjNtjN pppp . (6)
Further, if the prices of tradables are the same under the usual
arbitrage argument and in the
absence of border effects (Engel and Rogers, 1996), then the
relative price level is merely
proportional to the relative price of nontradables. In this
case, the price-income relationship
essentially reflects the link between prices of nontradables and
income levels. Of course,
prices of tradables are not necessarily identical across
regions. Nevertheless, if prices of
tradables, compared with prices of nontradables, are more likely
to converge, then the income
effect should be more pronounced on prices of nontradables than
tradables.
The implication of the degree of tradability is examined using
the specification:
, , , , ,k j t k k j t k j tq y , (7)
where , ,k j tq is the relative price index of product category
k in region j at time t derived
based on the procedure defined by (3) using data on the
corresponding sub-price index of the
RDICP. An overarching issue is how to determine which product
category is tradable and
which is nontradable. The dichotomy between nontradables and
tradables is a convenient
device in theoretical analyses. In reality, however, most if not
all consumer products contain
both non-tradable and tradable components. Products are neither
strictly tradable nor
nontradable, but have different degrees of tradability. Thus, as
an empirical classification
scheme, the dichotomy of nontradables and tradables is quite
restrictive. With the caveat in
mind, we use data on price indexes of different product
categories to assess the role of
tradability.
The list of prefecture product-category price indexes is given
in the Appendix, Table
A-2. The data on these prefectural sub-indexes of the RDICP are
published every five years
and available only for 1997, 2002, and 2007 during the sample
period under consideration.
The year-by-year income effect coefficient estimates, k̂ s, from
product-category-specific
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price index data are presented in Table 1 and graphed in Figure
3. The estimates from the
prefectural consumer price level data are included for
comparison purposes. The last column
of Table 1 additionally reports the estimates by pooling the
data from the three sample years.
A few observations are in order.
First, in view of the disaggregated prices listed in Table A-2,
the category “services”
is commonly conceived to be less tradable than the category
“goods.” Indeed, in all years, the
income effect coefficient estimate of the “services” category is
larger than that of the “goods”
category. Further, the former is statistically significant while
the latter is not. The results are
in line with the notion that the Penn effect is driven by
nontradables.
Second, the “goods” group consists of products that are not
equally tradable. Even
though data on “goods” have an insignificant k̂ estimate, the
sub-categories “agricultural
& aquatic products” and “fresh agricultural & aquatic
products” display a significant
price-income relationship for 1997 and 2002.
The results could be attributed to their perishable
characteristic. These two perishable
sub-categories are likely to have a lower degree of tradability
than, say, industrial products,
and exhibit the Penn effect like a nontradable product.
According to k̂ estimates, the group
of “fresh agricultural & aquatic products” yields a stronger
income effect than the group of
“agricultural & aquatic products.” The improvements in
transportation and storage
technologies enhance the tradability of perishable products, and
thus, weaken the Penn effect
in the 2007 sample. It is also noted that, the income effect
exhibited by the “CPI excluding
fresh foods” category is weaker than the one by the “CPI”
data.
For the 1997 and 2002 regressions, the income displays no
significant effect on the
prices of the subcategory “industrial products,” which are in
general nonperishable and
perceived to be highly tradable. Nevertheless, the income effect
became significant in 2007.
While we do not have a definitive explanation for the switch in
significance over time, the
results are suggestive of the possibility that the degree of
tradability can vary not only across
product categories but also over time.
The income effect estimate for “publications” is insignificant.
Products in this
sub-category including books, magazines and newspapers, tend to
have nation-wide listed
prices. Such practices limit the variability of regional prices,
and make the product prices
unresponsive to income changes.
The significantly negative coefficient estimates obtained for
the “electricity, gas &
water charges” sub-category deserves a comment. While this
sub-category is included under
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the heading of “goods,” its components are mostly utilities, and
their prices are subject to
local administrations and regulations. Water, for example, is
usually supplied by municipal
governments, whereas electricity and gas are by monopolistic
firms in geographically defined
markets. Thus, these prices are less likely subject to the usual
arbitrage forces.
The culprit of negative coefficient estimates could be the
economies of scale effect
underlying the provision of public services and utilities. For
instance, if there is a large fixed
cost of providing electricity and gas services, the average
utility charge can decline with the
population and the number of households using the services. In
our prefectural dataset, the
population size is positively correlated with the income level.
Thus, compared with less
affluent prefectures, more affluent prefectures can have lower
utility charges.7
Third, by the same token, products within the “services”
category have different
degrees of tradability. The “public services” and “general
services” sub-categories have
starkly different income effects. The “public services” include
public housing, medical and
welfare, communication and transportation, and educational
services. These services are
generally not tradable between prefectures, and their prices
tend to be regulated. Our results
show that the prices of “public services” are income
insensitive. On the other hand, the price
of privately provided “general services” exhibits a highly
significant and large income effect.
That is, the price of “general services” tends to be higher
where real income is higher.
The two subgroups of “general services;” namely, the “private
house rent” and “eating
out” differ substantially in their income coefficient estimates.
While both k̂ s are statistically
significant, the estimated income effect on the subgroup of
“private house rent” is much
stronger than on the subgroup of “eating out” prices. One
speculation is that prevalence of
chain-stores in the eating out industry weakens the income
effect on its price.
The results pertaining to the pooled data are essentially the
same as those discussed
above. The main exception is that the income effect is
significant for the “goods” category,
albeit the magnitude is relatively small. The significance can
be attributed to the increase in
estimation efficiency due to an increase in sample size, and the
fact that not all items under
the category are tradable.
Overall, the prices of products with different degrees of
tradability respond differently
to income. The Japanese prefectural data yield results that
confirm the common wisdom;
income tends to have a larger impact on prices of nontradables
than on prices of tradables. An
7 Indeed, on the average, the prefectural price of “electricity,
gas & water charges” is lower in prefectures with a larger
population size. These results are available upon request.
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implication is that the observed positive association between
price and income levels is
largely attributable to nontradables. Of course, the
interpretation is subject to the usual caveat
that we do not have a precise measure of the degree of product
tradability.
5. Accounting for the Intra-Japan Penn effect
5.1 Productivity and Economic Density
The difference in the relative sectoral productivity is the
basis of the B-S hypothesis,
which is a long-standing explanation of the international
price-income relationship. 8
Empirical studies on the productivity differential effect have
evolved over time. One key
issue is the choice of productivity measure, which has varied
from per capita gross national
product to some specifically constructed measures of sectoral
productivity.9 Further, some
studies consider (average) labor productivity while others use
total factor productivity.10 The
comparison of levels of national productivity is further
complicated by differences in
methods of reporting economic data and in data quality.
Productivity is not directly observable in general. While
empirical measures of
productivity are routinely used, there are concerns about how
well the empirical measures can
capture the notion of productivity used in theoretical models.
Indeed, because of the paucity
of the Japanese prefectural productivity data, we explore
alternative proxies for
productivity. 11 Specifically, we consider the proxies that are
motivated by studies on
economic density (Carlino and Voith, 1992; Ciccone and Hall,
1996), and the related
agglomeration argument (Henderson, 1974; Krugman, 1991; Glaeser,
2008).
Economic density refers to the intensity of labor, human
capital, and physical
investment relative to the physical space. Ciccone and Hall
(1996) note a few channels
through which economic density can affect the level of
productivity in a locality:
rising-by-distance transport costs from one production stage to
the next; externalities
associated with physical proximity of production; and a high
degree of beneficial
8 Other explanations advocated in the literature include the
factor-intensity and factor- endowment approach (Kravis and Lipsey,
1983; Bhagwati, 1984), and the non-homothetic demand structure
approach (Bergstrand 1991). 9 For different choices of productivity
measures, see, for example, Balassa (1964), Officer (1976), Hsieh
(1982), Asea and Mendoza (1994), De Gregorio et al. (1994),
Canzoneri et al. (1999), Chinn (2000), and Kakkar (2003). 10 For
example, Marston (1987) and Canzoneri, Cumby, and Diba (1999) use
average labor productivity, while Asea and Mendoza (1994) and De
Gregorio et al. (1994) use total factor productivity. 11
Prefectural data constraints are quite severe. We explored the use
of proxy measures for labor productivity that are constructed using
incomplete prefectural data on sectoral value added and employment.
The results obtained from these noisy measures – not reported for
brevity but available from the authors – are mostly
insignificant.
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specialization possible in areas of dense activity. One
prediction of their analyses is that a
locality with a higher average employment density and a higher
inequality of employment
density will have a higher level of productivity. There is a
caveat however. Increasing
economic density generates not only agglomeration effects that
raise productivity, but also
congestion effects. If congestion effects outweigh agglomeration
effects, then a high density
area will have a low level of productivity. It is an empirical
matter to determine which of the
two effects prevails. Using the US state and county data, the
authors find that a rise in
employment density leads to a significant increase of average
labor productivity.12
5.2 Empirical Exploration
Because prefectural employment density data are not available,
we capture the
economic density effect using a) the prefectural population
density, and b) the population
density of the most agglomerated areas within a prefecture. The
second variable is based on
the population data of densely inhabited districts (DIDs), which
are districts that have more
than four thousands inhabitants per square kilometer. The two
variables correspond to the
average employment density and the employment density inequality
in Ciccone and Hall
(1996). To control for differences between employment and
population data, we include data
on unemployment rates in our analysis.13
The economic density effects are examined using the
regression
, 1 , 2 , 3 , ,j t j t j t j t j tq density DID UE , (8)
where tjdensity , and ,j tDID are, respectively, the number of
inhabitants per square
kilometer in prefecture j and in DIDs in the same prefecture at
time t. Similarly to the price
and income variables, the density variables are in logarithmic
terms and expressed as
deviations from their respective averages. ,j tUE is the
unemployment rate deviations from
the average at time t.
The data on population density and DIDs are available only every
five years, and for
1995, 2000, and 2005 during our sample period. Thus, 1995, 2000,
and 2005 density data are
paired up with the corresponding 1997, 2002, and 2007
disaggregated price data. We estimate
(8) using a) year-by-year cross-sectional data, and b) the
pooled data while allowing for
12 In a similar vein, Carlino and Voith (1992) find that total
factor productivity across the U.S. states increases with the level
of urbanization, and Glaeser and Maré (2001) report evidence on
labor productivity and wages. 13 An implicit assumption is that
unemployment rates, while varying across prefectures, are constant
across sectors within each prefecture. Ideally, one should use
employment data that are sector-and-prefecture-specific to
calculate employment density. However, these data are not
available.
-
12
year-specific intercepts. To conserve space, we focus on pooled
data estimations, and present
the year-by-year regression results in the appendix.
According to the economic density reasoning, we expect the two
density variables to
have positive effects. Assuming that the unemployment rate is
constant, a prefecture with a
high population density (represented by ,j tdensity ) has a high
average employment density
that implies a high level of productivity, a high level of
income, and hence, a high general
price level. When the average density is held constant, ,j tDID
reflects the extent of density
inequality within a prefecture since it captures essentially the
district-specific highest density.
A theoretical prediction is that, for a given level of average
density, density inequality within
a prefecture intensifies the overall effect and boosts the level
of productivity. Thus, ,j tDID
is also expected to exert a positive effect on prices. We expect
,j tUE to have a negative
effect; a high unemployment rate means a low effective
employment density, ceteris paribus.
The pooled estimates are summarized in Table 2. As column 1
presents, the average
density and DID density variables are jointly significant and
positive. The results are in
accordance with Ciccone and Hall (1996); that is, the two
density variables convey different
types of information about price levels. Under the presumption
that the economic density
variables are proxies for productivity levels, the finding lends
support to the link between
productivity and price levels. That is, a prefecture with a high
level of economic activity and
economic activity inequality tends to have a high general price
level. The unemployment rate
variable has a significantly negative coefficient estimate as
expected. The combined
explanatory power of these three variables is quite high at the
60% mark.
Do the density effects fully account for the intra-Japan Penn
effect? Column 2
evaluates the marginal effect of the income variable. When the
income variable is added to
(8), the DID variable retains its significance while the average
density variable becomes
statistically insignificant. The results indicate that the price
information content of the income
variable dominates that of the average density, and is not
identical to the DID density variable.
In terms of marginal explanatory power, inclusion of the income
variable leads to
improvement of the adjusted R-squared estimates albeit
relatively small.
Columns 3 to 5 compare the individual effects of the density and
income variables.14
Individually, they all display highly significant price effects.
The DID variable coupled with
14 To capture the employment density effect, the average density
and DID density variables are accompanied by the unemployment rate
variable.
-
13
the unemployment rate offers the highest explanatory power among
these three specifications,
while the income variable offers the lowest.
Table 3 presents the correlation coefficients between the
explanatory variables. The
average density variable exhibits sizable correlations of .77
and .58, respectively, with the
DID density and income variables. The correlation between the
DID density and income
variables is lower at .33. The insignificance of the average
density effect under column 2 of
Table 2 is possibly due to its relatively high degrees of
correlation with the other two
variables. While there is overlapping in price informational
contents, the combined
specification considered under column 2 shows that the empirical
Penn effect cannot be
entirely explained by economic density factors.
The year-by-year results, summarized in Table A-3 in the
appendix, convey a very
similar message. In general, the average density and DID density
variables are jointly
significant. The significance of the average density variable is
weakened in the presence of
the income variable, while that of the DID density variable is
not. The relative individual
effects and explanatory powers are comparable to those presented
in Table 2.
Similar to studies of the B-S effect, we assess the roles of
economic density in
explaining the relative price of nontradables to tradables using
the regression specification:
, , , , 1 , 2 , 3 , ,( )N j t T j t j t j t j t j tq q density
DID UE , (9)
where subscripts N and T denote nontradables and tradables
sectors, respectively.
We note that the two density variables in (9) are not
sector-specific and, hence, are not
direct measures of the sectoral productivity differentials.
However, if cross-prefecture
productivity differences in nontradables sectors are negligible
as assumed under the B-S
hypothesis, then the economic density variables reflect
differences in the productivity levels
of tradables sectors. Under this assumption, the productivity
differential effect argument
implies that 01 and 02 . The assumption and its limitations need
to be taken into
account when interpreting the empirical results.
The measure of the relative price of nontradables to tradables
is based on the relevant
sectoral price indices. Based on the results in section 4, we
use the price index of “general
services” as our proxy for the price of nontradables , ,N j tq ,
and the price indices of “industrial
products” and “goods” as two alternative proxies for the price
of tradables.
In Table 4, panels A and B summarize the pooled estimates for
the relative prices
based on “industrial products” and “goods”, respectively, as
tradables. As displayed in
column 1, the density variables jointly attain the expected
highly significant positive
-
14
coefficient estimates. Further, the adjusted R-squared estimate
suggests that the density
variables along with the unemployment rate variable explain
about 60% of the variations in
the relative price of nontradables to tradables between the
Japanese prefectures.
Some previous international studies report significant demand
side effects in
modelling the relative nontradable prices. For instance, De
Gregorio et al. (1994) use per
capita income as a demand shifter, rather than as a productivity
proxy. The results of
including the income variable in (9) are presented in column 2.
The influences of the
presence of the income variable are similar to those revealed by
the general price level
estimation (column 2 of Table 2); that is, the average density
variable becomes insignificant
while the DID density variable is still significant. The
marginal contribution of the income
variable to the overall explanatory power is relatively small in
magnitude, albeit the estimate
of its coefficient is statistically significant.15
Columns 3 to 5 indicate that the economic density and income
variables are
individually significant with the expected positive effect on
the relative prices. The results do
not depend on the choice of the proxy for tradable price index.
The adjusted R-squared
estimates suggest that the economic density variables, as
compared to the income, have a
higher degree of explanatory power. Overall, the results of the
relative price regressions
(Table 4) are qualitatively comparable to those of the general
price regressions (Table 2).16
5.3 Discussion – Economic Density and Prices
In the previous sub-section, we found that the two proxies for
economic density have
significant positive effects on the Japanese prefecture relative
price of nontradables to
tradables. Under the presumption that economic density is
related to productivity (Ciccone
and Hall, 1996), the finding implies that price differentials
are related to productivity
differentials. If productivity gains tend to concentrate in the
tradables sector, then the
inference could be extended to the context of sectoral
productivity differentials.
While the economic density variables capture productivity
effects, the mechanism
through which economic density affects the relative price of
nontradables to tradables is not
15 We also considered the real government expenditure share of
GPI as an additional control for demand side effects (Froot and
Rogoff, 1991; De Gregorio et al., 1994). However, its effect is not
found significant in any case. Further, the government expenditure
variable exhibits a strong negative correlation with per capita
income (-.81 by the pooled sample), tending to mask the effect of
the income variable. To conserve space, these additional results
are not reported but are available upon request. 16 With some minor
yearly variations, the year-by-year estimation results summarized
in Tables A-4-1 to A-4-3 in the appendix are qualitatively similar
to the results from pooled data reported in the text.
-
15
identical to the one underlying the standard B-S explanation.
One possible transmission
channel is as follows. The agglomeration of economic activities
promotes economic
opportunities and induces productivity gains in the locality.
The productivity gains, in turn,
impose pressure on wages in the sector of tradables (Glaeser and
Maré, 2001) and, assuming
inter-sectoral labor mobility, in the sector of nontradables.
Higher wages attract workers to
the region, resulting in an increase in the population density.
The growing population density
in turn propels the demand for locality-specific nontradables
including housing and other
locally-provided services. Prices of nontradables experience an
upward pressure because
there is an increase in demand and in input costs including
rents.
Under this setup, even though one observes co-movement between
income and the
general price level, the prices of nontradables are affected by
both supply and demand
factors.17 Under the B-S framework, nontradables are produced
using labor and capital that
have an elastic supply. The economic density approach, however,
recognizes the possible role
of inelastic supply of land in affecting the prices of
nontradables.18
The increase in production costs that include land prices and
rents will provide
incentives to improve labor productivity in the nontradables
sector. The economic
propagation mechanism underlying the economic density
exposition, thus, suggests that the
variation in population density can be a proxy for factors that
drive nontradables prices, and a
locality’s population density should be related to its
nontradables productivity and income, in
addition to its general price level. Both demand and supply
factors can be in action. Thus, the
empirical economic density effect could be driven by both demand
and supply forces, and not
necessary the same as the supply-side-driven B-S effect. Our
empirical findings, nevertheless,
show that the Penn effect represented by the income effect is
not entirely explained by
economic density.
6. Concluding Remarks
The Japanese prefectural data are employed to investigate the
price-income
relationship, which is known as the Penn effect. Compared with
most cross-country analyses,
one advantage of using the Japanese data is that the empirical
finding is less likely to be
affected by product quality differentials as the Japanese prices
are measured rather precisely
and consistently. In addition, the use of the intra-national
data effectively eliminates nominal
17 It is implicitly assumed that different regions have a
similar level of non-labor income. 18 In the B-S model,
inter-regional perfect mobility and, hence, elastic supply of
capital play an essential role in deriving the result that the
regional prices of nontradables are determined solely by supply
factors.
-
16
exchange rate volatility that could distort the observed link
between price and income levels
across locations. Thus, our investigation offers a less
ambiguous way to infer the prevalence
and robustness of the Penn effect, which is commonly documented
in cross-country studies.
Our empirical results reveal that the widely documented
cross-country positive
price-income association is also a staple feature of the
Japanese data. The observed
intra-Japan Penn effect resembles the international one in that
it is driven mainly by the
behavior of the prices of nontradables rather than
tradables.
In accounting for the intra-Japan Penn effect, we draw on
studies of economics of
agglomeration and, specifically, implications of economic
density on productivity. The notion
of economic density offers an alternative way to infer the link
between productivity, income,
and price levels that is different from the usual B-S
interpretation.
We find strong evidence that the relative prices of nontradables
to tradables in Japan
are driven by regional economic density characteristics. The
empirical economic density
variables are found to possess large incremental explanatory
power. For most specifications
considered, the economic density variables explain about 60% or
more of the variation in the
Japanese prefectural price differential of nontradables and
tradables. Although the income
effect on (relative) prices is weakened in the presence of
economic density variables, the
intra-Japan Penn effect cannot be totally explained by the
productivity-cum-economic-density
nexus. In other words, the income and density variables we
adopted contain some
non-overlapping information about prices. Informational contents
of per capita income
differentials can be broad and multifaceted. A higher income
level can be simultaneously an
outcome of a higher productivity level and a source of a greater
demand for goods and
services. Since our economic density variables also reflect both
demand and supply factors, it
is possible that they cover different facets of demand and
supply forces that drive price
variability. Our results warrant a future study on the roles of
the B-S hypothesis and the
agglomeration and economic density approach in explaining the
Penn effect.19
19 As illustrated in Appendix A3, the income effect on prices
among rich prefectures is different from the one among poor
prefectures. It is another area warrants additional analyses.
-
Appendix
Appendix A1. Data Sources
The Japanese regional data are obtained from the Regional
Statistics Database of the
Statistics Bureau, Ministry of Internal Affairs and
Communications. The international data
are obtained from the PWT 7.0 and the World Development
Indicators database (January
2012).
-
Appendix A2. Additional Tables Table A-1. Relative consumer
prices and per capita gross prefectural incomes 1996-2008
id Prefecture ,.jq ,.jy
1 Hokkaido 0.014 -0.065 2 Aomori 0.001* -0.182 3 Iwate -0.007
-0.097 4 Miyagi -0.003* -0.028 5 Akita -0.024 -0.115 6 Yamagata
0.006* -0.080 7 Fukushima -0.010 0.030 8 Ibaraki -0.009 0.041 9
Tochigi 0.004 0.082 10 Gunma -0.026 -0.002* 11 Saitama 0.025 0.023
12 Chiba 0.006 0.043 13 Tokyo 0.085 0.498 14 Kanagawa 0.070 0.152
15 Niigata 0.006 0.011 16 Toyama -0.003* 0.138 17 Ishikawa 0.006*
0.092 18 Fukui -0.004 0.045 19 Yamanashi 0.000* -0.035 20 Nagano
-0.013 0.047 21 Gifu -0.013 -0.013 22 Shizuoka 0.030 0.123 23 Aichi
0.026 0.248 24 Mie -0.008 0.103 25 Shiga -0.008 0.162 26 Kyoto
0.035 0.019 27 Osaka 0.054 0.127 28 Hyogo 0.022 0.037 29 Nara
-0.002* -0.092 30 Wakayama 0.003 -0.112 31 Tottori -0.021 -0.089 32
Shimane 0.007 -0.097 33 Okayama 0.010 0.027 34 Hiroshima -0.012
0.062 35 Yamaguchi -0.015 0.033 36 Tokushima -0.028 -0.031 37
Kagawa -0.018 -0.020 38 Ehime -0.039 -0.088 39 Kochi -0.015 -0.233
40 Fukuoka 0.002* -0.057 41 Saga -0.023 -0.111 42 Nagasaki 0.014
-0.209 43 Kumamoto -0.018 -0.177 44 Oita -0.022 -0.010* 45 Miyazaki
-0.047 -0.186 46 Kagoshima -0.007 -0.194 47 Okinawa -0.049
-0.285
-
Notes: The entries are 1996-2008 averages of relative consumer
prices and real per capita gross prefectural incomes. For each
year, prefectural price and income levels are measured in logged
deviations from their all prefecture averages. The entries with “*”
are statistically not different from zero at the 5 % significance
level.
Table A-2. Product categories of disaggregated regional price
indexes
Goods Agricultural & aquatic products
Fresh agricultural & aquatic products Industrial products
Electricity, gas & water charges Publications
Services Public services General services
Private house rent Eating out
-
Table A-3. Density effects on the price level by year
A. 1997 1 2 3 4 5 Average density .011**
(.004) .005 (.006)
.024** (.004)
DID density .076** (.016)
.075** (.014)
.113** (.016)
Unemployment rate
-.008* (.003)
-.005 (.004)
-.005 (.004)
-.008* (.004)
Income .055† (.029)
.138** (.029)
Adjusted R2
.685 .703 .548 .626 .425
B. 2002 1 2 3 4 5
Average density .008* (.004)
.005 (.006)
.017** (.004)
DID density .053** (.015)
.053** (.014)
.080** (.015)
Unemployment rate
-.010* (.003)
-.007 (.005)
-.007 (.004)
-.010* (.004)
Income .027 (.038)
.100** (.029)
Adjusted R2
.514 .512 .417 .336 .296
C. 2007 1 2 3 4 5
Average density .007 (.004)
.002 (.005)
.019** (.004)
DID density .060** (.017)
.061** (.016)
.085** (.013)
Unemployment rate
-.010** (.002)
-.006* (.003)
-.007** (.002)
-.010** (.002)
Income .055* (.027)
.128** (.022)
Adjusted R2 .603 .624 .509 . 585 .427
Notes: The table summarizes the estimation results of (8) in the
main text by year. Heteroskedastic-consistent standard errors are
provided in parentheses underneath the corresponding estimates. **
and * indicate statistical significance at the 1 and 5 % levels,
respectively.
-
Table A-4-1. Density effects on relative sectoral prices – the
1997 sample
1 2 3 4 5 A. Industrial products
Average density
.046** (.009)
.022† (.013)
.081** (.010)
DID density .209** (.039)
.205** (.039)
.356** (.047)
Unemployment rate -.015† (.008)
-.003 (.010)
-.006 (.010)
-.015 (.010)
Income .200* (.078)
.442** (.086)
Adjusted R2
.684 .706 .595 .599 .385
B. Goods
Average density
.048** (.009)
.025† (.013)
.081** (.011)
DID density .201** (.038)
.198** (.038)
.353** (.049)
Unemployment rate -.017† (.008)
-.004 (.011)
-.007 (.011)
-.017 (.011)
Income .194* (.075)
.444** (.084)
Adjusted R2
.700 .721 .614 .604 .407
Notes: The table summarizes the estimation results of (9) in the
main text and its variant specifications for the 1997 data.
Heteroskedastic-consistent standard errors are provided in
parentheses underneath the corresponding estimates. ** , * and †
indicate statistical significance at the 1 , 5 and 10 % levels,
respectively.
-
Table A-4-2. Density effects on relative sectoral prices – the
2002 sample 1 2 3 4 5 A. Industrial products
Average density
.025** (.008)
.012 (.010)
.054** (.008)
DID density .166** (.028)
.165** (.026)
.246** (.028)
Unemployment rate -.026** (.004)
-.017* (.007)
-.017** (.006)
-.027** (.005)
Income .120* (.048)
.309** (.058)
Adjusted R2
.743 .764 .593 .681 .428
B. Goods
Average density
.026** (.008)
.014 (.011)
.055** (.009)
DID density .168** (.028)
.167** (.025)
.251** (.030)
Unemployment rate -.028** (.004)
-.019* (.007)
-.019** (.006)
-.029** (.005)
Income .116* (.049)
.317** (.061)
Adjusted R2
.765 .784 .612 .699 .445
Notes: The table summarizes the estimation results of (9) in the
main text and its variant specifications for the 2002 data.
Heteroskedastic-consistent standard errors are provided in
parentheses underneath the corresponding estimates. ** and *
indicate statistical significance at the 1 and 5 % levels,
respectively.
-
Table A-4-3. Density effects on relative sectoral prices – the
2007 sample 1 2 3 4 5 A. Industrial products
Average density
.020* (.009)
.008 (.010)
.038** (.007)
DID density .088* (.037)
.089** (.032)
.155** (.028)
Unemployment rate -.012** (.003)
-.004 (.004)
-.009** (.002)
-.014** (.003)
Income .129* (.048)
.228** (.049)
Adjusted R2
.582 .624 .524 .532 .419
B. Goods
Average density
.021* (.008)
.009 (.010)
.041** (.007)
DID density .100** (.035)
.100** (.031)
.169** (.029)
Unemployment rate -.017** (.003)
-.009* (.004)
-.013** (.002)
-.019** (.003)
Income .125* (.046)
.260** (.048)
Adjusted R2
.661 .696 .592 .610 .489
Notes: The table summarizes the estimation results of (9) in the
main text and its variant specifications for the 2007 data.
Heteroskedastic-consistent standard errors are provided in
parentheses underneath the corresponding estimates. ** and *
indicate statistical significance at the 1 and 5 % levels,
respectively.
-
Appendix A3. Penn Effects Among Rich and Poor Prefectures
Some studies (Kravis and Lipsey, 1987; Cheung, Chinn, and Fujii,
2007; Fujii, 2013b)
suggest that the income effect on prices could vary between
economies at different stages of
development and is stronger for developed economies than for
developing ones. Since the
stage of development is closely related to the level of income,
the Penn effect tends to be
more substantial among higher income countries than lower income
countries. Does a similar
regularity hold in the intra-Japan context?
To investigate the issue, we rank the forty-seven Japanese
prefectures according to
their per capita income and construct two subsamples – the upper
and lower income groups
whose income levels are, respectively, above and below the
median level. The Penn effect
regression (5) was re-run on each of these two subsamples. The
year-by-year ̂ s graphed in
Figure A-1 clearly show that the Penn effect is mainly an upper
income group phenomenon.
The ̂ s from the upper income group are larger than those from
the lower income group and
those in Figure 1. More importantly, the upper income group
estimates are statistically
significant while the lower income group ones are not.
Figures A-2 and A-3 plot the year-by-year estimates, ̂ s, from
the upper and lower
income group samples constructed in a similar fashion using the
PWT (version 7.0) and the
WDI, respectively. While the numerical values are different from
those in Figure A-1, the
qualitative results pertaining to the upper and lower income
groups are the same. The upper
income group yields significant and large income effect
estimates while the lower income
group obtains insignificant and small estimates.
In sum, comparable to the results from the cross-country data,
the significant income
effect on prices displayed by the Japanese data appears to be
driven mainly by rich, rather
than poor, prefectures.
-
Figure A-1. Penn effects for the high and low income Japanese
Prefectures
Notes: The figure plots the Penn effect coefficient estimates
and their p-values of the high and low income Japanese prefectures
sub-samples obtained from (5) in the main text.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
2008
Upper income (coefficient) Lower income (coefficient) Upper
income (p-value) Lower income (p-value)
-
Figure A-2. Penn effects for high and low income sub-samples of
the PWT 7.0 data
Notes: The figure plots the Penn effect coefficient estimates
and their p-values of the high and low income sub-samples of the
PWT 7.0 data obtained from (5) in the main text.
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
2008
Upper (coefficient) Upper (p-value) Lower (coefficient) Lower
(p-value)
-
Figure A-3. Penn effects for high and low income sub-samples of
the WDI data
Notes: The figure plots the Penn effect coefficient estimates
and their p-values of the high and low income sub-samples of the
WDI 7.0 data obtained from (5) in the main text.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
2008
Upper (coefficient) Upper (p-value) Lower (coefficient) Lower
(p-value)
-
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Table 1. Penn effect by product category
1997 2002 2007 Pooled CPI 0.138**
(0.029) 0.100** (0.029)
0.128** (0.022)
0.122** (0.015)
CPI excluding fresh foods 0.094** (0.020)
0.073** (0.022)
0.105** (0.016)
0.092** (0.010)
Goods 0.025
(0.023) 0.047
(0.030) 0.040
(0.029) 0.038* (0.015)
Agricultural & aquatic products 0.154** (0.040)
0.174** (0.039)
0.066 (0.049)
0.127** (0.025)
Fresh agricultural & aquatic products
0.170** (0.048)
0.195** (0.044)
0.069 (0.054)
0.140** (0.028)
Industrial products 0.028 (0.026)
0.055 (0.033)
0.072* (0.033)
0.053** (0.017)
Publications 0.039 (0.029)
0.054 (0.033)
0.001 (0.025)
0.029 (0.016)
Electricity, gas & water charges -0.234** (0.058)
-0.204** (0.061)
-0.197** (0.058)
-0.211** (0.032)
Services 0.352**
(0.069) 0.229** (0.062)
0.185** (0.049)
0.252** (0.034)
Public services 0.032 (0.036)
-0.009 (0.019)
0.015 (0.014)
0.013 (0.013)
General services 0.470** (0.094)
0.365** (0.086)
0.300** (0.074)
0.374** (0.046)
Private house rent 1.341** (0.256)
0.957** (0.270)
0.864** (0.244)
1.044** (0.140)
Eating out 0.221** (0.059)
0.159** (0.035)
0.085** (0.024)
0.151** (0.024)
Notes: The table summarizes the estimation results of (7) in the
main text. Heteroskedastic-consistent standard errors are provided
in parentheses underneath the corresponding estimates. ** and *
indicate statistical significance at the 1 and 5 % levels,
respectively. Year-specific constants are allowed for the pooled
data estimation.
-
Table 2. Density effects on the price level – the pooled
estimates 1 2 3 4 5
Average density
0.009** (0.002)
0.004 (0.003)
0.020** (0.002)
DID density 0.061** (0.009)
0.061** (0.008)
0.092** (0.008)
Unemployment rate -0.009** (0.001)
-0.005** (0.002)
-0.006** (0.001)
-0.009** (0.001)
Income 0.051** (0.018)
0.122** (0.015)
Adjusted R2
0.600 0.623 0.492 0.555 0.386
Notes: The table summarizes the estimation results of (8) in the
main text and its variant specifications using sample of the 1997,
2002, and 2007 data. Year-specific constants are included in all
specifications. The number of observations is 141.
Heteroskedastic-consistent standard errors are provided in
parentheses underneath the corresponding estimates. ** and *
indicate statistical significance at the 1 and 5 % levels,
respectively.
-
Table 3. Correlations between explanatory variables
Income Average density DID density
Average density 0.58
DID density 0.33 0.77
Unemployment rate -0.36 0.28 0.42
Notes: The table gives correlation coefficient estimates between
explanatory variables considered in the main text. These estimates
are computed using data pooled from the 1997, 2002, and 2007
samples.
-
Table 4. Density effects on relative sectoral prices – the
pooled estimates 1 2 3 4 5 A. Industrial products
Average density
0.031** (0.006)
0.011 (0.007)
0.056** (0.005)
DID density 0.140** (0.023)
0.140** (0.022)
0.240** (0.022)
Unemployment rate -0.014** (0.003)
-0.002 (0.004)
-0.008** (0.003)
-0.016** (0.003)
Income 0.186** (0.036)
0.321** (0.039)
Adjusted R2
0.598 0.642 0.520 0.528 0.372
B. Goods
Average density
0.033** (0.006)
0.013 (0.006)
0.058** (0.005)
DID density 0.143** (0.021)
0.143** (0.020)
0.248** (0.022)
Unemployment rate -0.017** (0.003)
-0.006 (0.004)
-0.011** (0.003)
-0.019** (0.003)
Income 0.179** (0.034)
0.336** (0.037)
Adjusted R2
0.633 0.674 0.552 0.557 0.409
Notes: The table summarizes the estimation results of (9) in the
main text and its variant specifications using sample of the 1997,
2002, and 2007 data. Year-specific constants are included in all
specifications. The number of observations is 141.
Heteroskedastic-consistent standard errors are provided in
parentheses underneath the corresponding estimates. ** and *
indicate statistical significance at the 1 and 5 % levels,
respectively.
-
Figure 1. Time profile of the Penn effect within Japan
Notes: The figure plots the Penn effect coefficient estimates
and their p-values of the Japanese data obtained from (5) in the
main text.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
20080
0.0005
0.001
0.0015
0.002
0.0025
Penn coefficient (left scale) P-value (right scale)
-
Figure 2. The international and intra-Japan Penn effects
Notes: The figure plots the Penn effect coefficient estimates
and their p-values of a) the international PWT7.0 and WDI (January
2012) data and b) the Japanese data obtained from (5) in the main
text.
0
0.05
0.1
0.15
0.2
0.25
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
2008
Intra-Japan PWT7.0 WDI
-
Figure 3. Income effects on the Japanese disaggregated price
indexes
Notes: The figure plots the estimates of income effect on price
indexes of disaggregated product categories obtained from (7) in
the main text.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6CP
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1997 2002 2007